
def 							A__       (    lowerCamelCase  ,     lowerCamelCase    )	->						int:
				UpperCamelCase_:				List[Any]						=    1  # To kept the Calculated Value
				# Since C(n, k) = C(n, n-k)
				if k > (n - k):
								UpperCamelCase_:				Optional[int]						=    n - k
				# Calculate C(n,k)
				for i in range(lowerCamelCase    ):
								result *= n - i
								result //= i + 1
				return result







def 							A__       (    lowerCamelCase    )	->						int:
				return binomial_coefficient(2 * node_count  ,     lowerCamelCase    ) // (node_count + 1)







def 							A__       (    lowerCamelCase    )	->						int:
				if n < 0:
								raise ValueError("""factorial() not defined for negative values"""    )
				UpperCamelCase_:				int						=    1
				for i in range(1  ,     n + 1    ):
								result *= i
				return result







def 							A__       (    lowerCamelCase    )	->						int:
				return catalan_number(lowerCamelCase    ) * factorial(lowerCamelCase    )


if __name__ == "__main__":
							lowerCamelCase_    :			Optional[Any]    =	int(input("""Enter the number of nodes: """).strip() or 0)
							if node_count <= 0:
														raise ValueError("""We need some nodes to work with.""")
							print(
							    F"""Given {node_count} nodes, there are {binary_tree_count(node_count)} """
							    F"""binary trees and {catalan_number(node_count)} binary search trees."""
							)








import torch

from diffusers import CMStochasticIterativeScheduler

from .test_schedulers import SchedulerCommonTest

class 							_UpperCamelCase					(       _A	):






			'''simple docstring'''

			__UpperCamelCase   :    Tuple          =			(CMStochasticIterativeScheduler,)
			__UpperCamelCase   :    List[str]          =			10

			def    lowerCAmelCase__						(							self			:							Optional[int]    ,						**snake_case_			:							List[str]   ):
							UpperCamelCase_:				Optional[int]						=    {
							    """num_train_timesteps""": 201,
							    """sigma_min""": 0.002,
							    """sigma_max""": 80.0,
							}

							config.update(**snake_case_   )
							return config

			def    lowerCAmelCase__						(							self			:							Tuple   ):
							UpperCamelCase_:				Tuple						=    10

							UpperCamelCase_:				Tuple						=    self.get_scheduler_config()
							UpperCamelCase_:				List[str]						=    self.scheduler_classes[0](**snake_case_   )

							scheduler.set_timesteps(snake_case_   )

							UpperCamelCase_:				int						=    scheduler.timesteps[0]
							UpperCamelCase_:				str						=    scheduler.timesteps[1]

							UpperCamelCase_:				Optional[int]						=    self.dummy_sample
							UpperCamelCase_:				int						=    0.1 * sample

							UpperCamelCase_:				Optional[Any]						=    scheduler.step(snake_case_    ,						snake_case_    ,						snake_case_   ).prev_sample
							UpperCamelCase_:				Any						=    scheduler.step(snake_case_    ,						snake_case_    ,						snake_case_   ).prev_sample

							self.assertEqual(output_a.shape    ,						sample.shape   )
							self.assertEqual(output_a.shape    ,						output_a.shape   )

			def    lowerCAmelCase__						(							self			:							Optional[Any]   ):
							for timesteps in [10, 50, 100, 1000]:
											self.check_over_configs(num_train_timesteps=snake_case_   )

			def    lowerCAmelCase__						(							self			:							Optional[Any]   ):
							for clip_denoised in [True, False]:
											self.check_over_configs(clip_denoised=snake_case_   )

			def    lowerCAmelCase__						(							self			:							Any   ):
							UpperCamelCase_:				Any						=    self.scheduler_classes[0]
							UpperCamelCase_:				List[str]						=    self.get_scheduler_config()
							UpperCamelCase_:				Tuple						=    scheduler_class(**snake_case_   )

							UpperCamelCase_:				Optional[int]						=    1
							scheduler.set_timesteps(snake_case_   )
							UpperCamelCase_:				Any						=    scheduler.timesteps

							UpperCamelCase_:				int						=    torch.manual_seed(0   )

							UpperCamelCase_:				Any						=    self.dummy_model()
							UpperCamelCase_:				Union[str, Any]						=    self.dummy_sample_deter * scheduler.init_noise_sigma

							for i, t in enumerate(snake_case_   ):
											# 1. scale model input
											UpperCamelCase_:				str						=    scheduler.scale_model_input(snake_case_    ,						snake_case_   )

											# 2. predict noise residual
											UpperCamelCase_:				List[Any]						=    model(snake_case_    ,						snake_case_   )

											# 3. predict previous sample x_t-1
											UpperCamelCase_:				str						=    scheduler.step(snake_case_    ,						snake_case_    ,						snake_case_    ,						generator=snake_case_   ).prev_sample

											UpperCamelCase_:				Union[str, Any]						=    pred_prev_sample

							UpperCamelCase_:				int						=    torch.sum(torch.abs(snake_case_   )   )
							UpperCamelCase_:				List[Any]						=    torch.mean(torch.abs(snake_case_   )   )

							assert abs(result_sum.item() - 192.7614   ) < 1e-2
							assert abs(result_mean.item() - 0.2510   ) < 1e-3

			def    lowerCAmelCase__						(							self			:							str   ):
							UpperCamelCase_:				Dict						=    self.scheduler_classes[0]
							UpperCamelCase_:				Tuple						=    self.get_scheduler_config()
							UpperCamelCase_:				List[Any]						=    scheduler_class(**snake_case_   )

							UpperCamelCase_:				str						=    [106, 0]
							scheduler.set_timesteps(timesteps=snake_case_   )
							UpperCamelCase_:				int						=    scheduler.timesteps

							UpperCamelCase_:				List[Any]						=    torch.manual_seed(0   )

							UpperCamelCase_:				List[Any]						=    self.dummy_model()
							UpperCamelCase_:				int						=    self.dummy_sample_deter * scheduler.init_noise_sigma

							for t in timesteps:
											# 1. scale model input
											UpperCamelCase_:				Optional[int]						=    scheduler.scale_model_input(snake_case_    ,						snake_case_   )

											# 2. predict noise residual
											UpperCamelCase_:				Dict						=    model(snake_case_    ,						snake_case_   )

											# 3. predict previous sample x_t-1
											UpperCamelCase_:				str						=    scheduler.step(snake_case_    ,						snake_case_    ,						snake_case_    ,						generator=snake_case_   ).prev_sample

											UpperCamelCase_:				List[str]						=    pred_prev_sample

							UpperCamelCase_:				Union[str, Any]						=    torch.sum(torch.abs(snake_case_   )   )
							UpperCamelCase_:				str						=    torch.mean(torch.abs(snake_case_   )   )

							assert abs(result_sum.item() - 347.6357   ) < 1e-2
							assert abs(result_mean.item() - 0.4527   ) < 1e-3

			def    lowerCAmelCase__						(							self			:							str   ):
							UpperCamelCase_:				int						=    self.scheduler_classes[0]
							UpperCamelCase_:				Optional[int]						=    self.get_scheduler_config()
							UpperCamelCase_:				Tuple						=    scheduler_class(**snake_case_   )

							UpperCamelCase_:				Any						=    [39, 30, 12, 15, 0]

							with self.assertRaises(snake_case_    ,						msg="""`timesteps` must be in descending order."""   ):
											scheduler.set_timesteps(timesteps=snake_case_   )

			def    lowerCAmelCase__						(							self			:							str   ):
							UpperCamelCase_:				Union[str, Any]						=    self.scheduler_classes[0]
							UpperCamelCase_:				Tuple						=    self.get_scheduler_config()
							UpperCamelCase_:				List[str]						=    scheduler_class(**snake_case_   )

							UpperCamelCase_:				Tuple						=    [39, 30, 12, 1, 0]
							UpperCamelCase_:				List[Any]						=    len(snake_case_   )

							with self.assertRaises(snake_case_    ,						msg="""Can only pass one of `num_inference_steps` or `timesteps`."""   ):
											scheduler.set_timesteps(num_inference_steps=snake_case_    ,						timesteps=snake_case_   )




			def    lowerCAmelCase__						(							self			:							int   ):
							UpperCamelCase_:				Any						=    self.scheduler_classes[0]
							UpperCamelCase_:				int						=    self.get_scheduler_config()
							UpperCamelCase_:				int						=    scheduler_class(**snake_case_   )

							UpperCamelCase_:				int						=    [scheduler.config.num_train_timesteps]

							with self.assertRaises(
							    snake_case_    ,						msg="""`timesteps` must start before `self.config.train_timesteps`: {scheduler.config.num_train_timesteps}}"""    ,						):
											scheduler.set_timesteps(timesteps=snake_case_   )






